Democratic Sen. Ron Wyden of Oregon — who coined Mnuchin's January statement as the "Mnuchin rule" — said Tuesday that he had seen a "very substantial retreat" on the issue. Wyden pointed to the Treasury secretary's Monday House testimony in which he said Trump will not veto a tax bill even if it gives a tax cut to the wealthiest Americans.

"Mr. Secretary, you made a commitment that there would be no absolute tax cut for the wealthy. And yesterday, you changed that. You said, we have an objective to do that. So maybe, it'll happen maybe it won't," Wyden said.

In Senate testimony on Tuesday, Mnuchin defended his position, saying the White House and Congress need to reach a compromise to pass a tax plan. A deal may not include all of President Donald Trump's priorities, he said.

Here is part of his exchange with Wyden:

Mnuchin: "Our focus is on getting tax reform done. To get tax reform done, it's my job to figure out what meets the president's objective, what meets the House and the Senate so that we can get something signed into law. And there will be compromises along the way on this. So, yes, you made it a rule, I didn't make it a rule. I was honored that you named it —

Wyden: No, no, no, Mr. Secretary, you took great pride as we repeated what you said and you again, 10 days ago, referenced the original comment by saying it on CNBC. You are the one who has walked it back. Nobody else has walked it back. You are the one who walked it back.

Mnuchin: I have walked it back from my CNBC interview. ... But we've had the opportunity to talk about this several times. And again, I look forward to coming to your office and talking about tax reform. And again, tax reform, at the end of the day, the president will evaluate what's on his desk and he'll make a decision whether he wants to sign it or not. My objective is to deliver tax reform so that we can get the economy back going.

The Trump administration says its plan to chop tax rates for businesses and individuals, along with rolling back regulations on companies, will kick-start the U.S. economy.